DotNetNuke.Services.Search.Entities.SearchDocumentToDelete doesn't seem to be supported in the 7.3.1 version of DotNetNuke.dll. However, I can see it in 7.4.2. I don't know when this method was introduced but right now, it's generating loads of exceptions.

Thanks Baldwin - I've applied the update to my development site and I haven't seen any more exceptions being generated. I'll be applying the update to my live site tomorrow - thanks again for the quick resolution :)